scholarly journals Characterization and stability analysis of advanced multi-quadratic functional equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abasalt Bodaghi ◽  
Hossein Moshtagh ◽  
Hemen Dutta
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Stability Analysis ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Technique ◽  
The Stability

AbstractIn this paper, we introduce a new quadratic functional equation and, motivated by this equation, we investigate n-variables mappings which are quadratic in each variable. We show that such mappings can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to the stability and hyperstability outcomes.

scholarly journals A Fixed Point Approach to the Stability of Pexider Quadratic Functional Equation with Involution

2010 ◽  
Vol 2010 (1) ◽  
pp. 839639 ◽  
Author(s):  
MM Pourpasha ◽  
JM Rassias ◽  
R Saadati ◽  
SM Vaezpour
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
The Stability

scholarly journals Stability of ann-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Random Normed Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang-Hi Lee ◽  
Soon-Mo Jung
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Mixed Type ◽  
Fixed Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Normed Spaces ◽  
Stability Problems ◽  
Random Normed Spaces ◽  
The Stability

We investigate the stability problems for then-dimensional mixed-type additive and quadratic functional equation2f(∑j=1nxj)+∑1≤i,j≤n,  i≠jf(xi-xj)=(n+1)∑j=1nf(xj)+(n-1)∑j=1nf(-xj)in random normed spaces by applying the fixed point method.

scholarly journals On the Stability of Quadratic Functional Equations inF-Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Xiuzhong Yang
Keyword(s):  
Functional Equation ◽  
Functional Equations ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
The Stability ◽  
Rassias Stability

The Hyers-Ulam-Rassias stability of quadratic functional equationf(2x+y)+f(2x-y)=f(x+y)+f(x-y)+6f(x)and orthogonal stability of the Pexiderized quadratic functional equationf(x+y)+f(x-y)=2g(x)+2h(y)inF-spaces are proved.

scholarly journals Hyers-Ulam Stability of Quadratic Functional Equation Based on Fixed Point Technique in Banach Spaces and Non-Archimedean Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2575
Author(s):  
Kandhasamy Tamilvanan ◽  
Abdulaziz M. Alanazi ◽  
Maryam Gharamah Alshehri ◽  
Jeevan Kafle
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
Fixed Point Technique ◽  
Fixed Point Techniques ◽  
Stability Results

In this paper, the authors investigate the Hyers–Ulam stability results of the quadratic functional equation in Banach spaces and non-Archimedean Banach spaces by utilizing two different techniques in terms of direct and fixed point techniques.

scholarly journals A FIXED POINT APPROACH TO THE STABILITY OF QUADRATIC FUNCTIONAL EQUATION

2006 ◽  
Vol 43 (3) ◽  
pp. 531-541 ◽  
Author(s):  
Soon-Mo Jung ◽  
Tae-Soo Kim ◽  
Ki-Suk Lee
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
The Stability

scholarly journals The Stability of a Quadratic Functional Equation with the Fixed Point Alternative

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Choonkil Park ◽  
Ji-Hye Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Method ◽  
Point Method ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Ulam Stability ◽  
The Stability

Lee, An and Park introduced the quadratic functional equationf(2x+y)+f(2x−y)=8f(x)+2f(y)and proved the stability of the quadratic functional equation in the spirit of Hyers, Ulam and Th. M. Rassias. Using the fixed point method, we prove the generalized Hyers-Ulam stability of the quadratic functional equation in Banach spaces.

A Fixed Point Approach to the Stability of Quadratic Functional Equations in Modular Spaces

2017 ◽  
Vol 6 (1) ◽  
pp. 171-175
Author(s):  
Seong Sik Kim ◽  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Functional Equations ◽  
Fixed Point Method ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
Modular Spaces ◽  
The Stability ◽  
Positive Integers ◽  
Rassias Stability

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equation f(kx + y) + f(kx – y) = 2k2f(x) + 2f(y) for any fixed positive integers k ∈ Ζ+ in modular spaces by using fixed point method.

scholarly journals Nearly Ternary Quadratic Higher Derivations on Non-Archimedean Ternary Banach Algebras: A Fixed Point Approach

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
M. Eshaghi Gordji ◽  
M. B. Ghaemi ◽  
J. M. Rassias ◽  
Badrkhan Alizadeh
Keyword(s):  
Functional Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Banach Algebras ◽  
Quadratic Functional Equation ◽  
Quadratic Functional ◽  
Fixed Point Approach ◽  
Ternary Algebras ◽  
The Stability

We investigate the stability and superstability of ternary quadratic higher derivations in non-Archimedean ternary algebras by using a version of fixed point theorem via quadratic functional equation.

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